arXiv subjects
Publications and source records attributed to D. A. Garanin.
Combination of the thermal effet in magnetic deflagration with resonance spin tunneling controlled by the dipole-dipole interaction in molecular magnets leads to the increase of the deflagration speed in the dipolar window near tunneling resonances.
We study a magnetic molecule that exhibits spin tunneling and is free to rotate about its anisotropy axis. Exact low-energy eigenstates of the molecule that are superpositions of spin and rotational states are obtained. We show that parameter $α= 2(\hbar S)^2/(IΔ)$ determines the ground state of the molecule. Here $\hbar S$ is the spin, $I$ is the moment of inertia, and $Δ$ is the tunnel splitting. The magnetic moment of the molecule is zero at $α< α_c = [1-1/(2S)^{2}]^{-1}$ and non-zero at $α> α_c$. At $α\to \infty$ the spin of the molecule localizes in one of the directions along the anisotropy axis.
Dissipative spin-tunneling transitions at biased resonances in molecular magnets such as Mn-12 Ac are controlled by the dipolar field that can bring the system on and off resonance. It is shown that this leads to spin relaxation in form of propagating fronts of tunneling, with the dipolar field adjusting self-consistently to provide a zero bias within the front core. There are two regimes of the front propagation: laminar and non-laminar with discontinuous magnetization and dipolar field. In the laminar regime the speed of the front can exceed that of the magnetic deflagration, if the transverse field is large enough. Fronts of tunneling can be initiated by magnetic field sweep near the end of the crystal.
We study low temperature resonant spin tunneling in molecular magnets induced by a field sweep with account of dipole-dipole interactions. Numerical simulations uncovered formation of self-organized patterns of the magnetization and of the ensuing dipolar field that provide resonant condition inside a finite volume of the crystal. This effect is robust with respect to disorder and should be relevant to the dynamics of the magnetization steps observed in molecular magnets.
By numerically solving the equations of motion for atomic spins we show that internal spin-wave processes in large enough magnetic particles, initially in unstable states, lead to complete magnetization reversal and thermalization. The particle's magnetization strongly decreases in the middle of reversal and then recovers. We identify two main scenarios, exponential and linear spin-wave instabilities. For the latter, the longitudinal and transverse relaxation rates have been obtained analytically. Orientation dependence of these rates leads to a nonexponential relaxation of the particle's magnetization at long times.
Local time-dependent theory of Einstein - de Haas effect is developed. We begin with microscopicinteractions and derive dynamical equations that couple elastic deformations with internal twists due to spins. The theory is applied to the description of the motion of a magnetic cantilever caused by the oscillation of the domain wall. Theoretical results are compared with a recent experiment on Einstein - de Haas effect in a microcantilever.
We find that dipolar interactions favor ferromagnetic ordering of elongated crystals of Mn12 Acetate below 0.8 K. Ordered crystals must possess domain walls. Motion of the wall corresponds to a moving front of Landau-Zener transitions between quantum spin levels. Structure and mobility of the wall are computed. The effect is robust with respect to inhomogeneous broadening and decoherence.
Spin relaxation between the two lowest-lying spin-states has been studied in the S=4 single molecule magnet Ni$_4$ under steady state conditions of low amplitude and continuous microwave irradiation. The relaxation rate was determined as a function of temperature at two frequencies, 10 and 27.8 GHz, by simultaneously measuring the magnetization and the absorbed microwave power. A strong temperature dependence is observed below 1.5 K, which is not consistent with a direct single-spin-phonon relaxation process. The data instead suggest that the spin relaxation is dominated by a phonon bottleneck at low temperatures and occurs by an Orbach mechanism involving excited spin-levels at higher temperatures. Experimental results are compared with detailed calculations of the relaxation rate using the universal density matrix equation.
Effective giant spins of magnetic nanoparticles are considered classically in the conventional theory of superparamagnetism based on the Landau-Lifshitz-Langevin equation. However, microscopic calculations for a large spin with uniaxial anisotropy, coupled to the lattice via the simplest generic mechanism, show that the results of the conventional theory are not reproduced in the limit S ->\infty. In particular, the prefactor Gamma_0 in the Arrhenius escape rate over the barrier Gamma =Gamma_0 exp[-Delta U/(k_B T)] has an anomalously large sensitivity to symmetry-breaking interactions such as transverse field
Landau-Zener (LZ) transitions of a two-level system (e. g., electronic spin in molecular magnets) coupled to one or many environmental spins (e. g., nuclear spins) are studied. For rather general interactions the LZ problem is reduced to that of a Landau-Zener grid. It is shown analytically that environmental spins initially in their ground state do not influence the staying probability P. This changes if they are prepared in a statistical ensemble. For a more specific model with environmental spins in a transverse field, LZ transitions are studied in the case of well-separated resonances in the LZ grid. The full evolution of the system is described as a succession of elemenary transitions at avoided crossings and free evolution between them. If the environmental spins are strongly coupled to the central spin, their effect on P is weak. In other cases LZ transitions are strongly suppressed and P is decreasing very slowly with the sweep-rate parameter epsilon ~ 1/v, v being the energy sweep rate.
The technique of density matrix equation (DME) for a small system interacting with a bath is explained in detail. Special attention is given to the nonsecular DME that is needed in the vicinity of overdamped tunnelling resonances in molecular magnets (MM). The relaxation terms of the DME for MM are represented in the universal form that does not employ any unknown spin-lattice coupling constants and absorbs the information about the spin Hamiltonian in the exact basis states and transition frequencies. This makes adding new types of anisotropy easy and error-free. The Mathematica code is available from the author.
A magnetic particle with atomic spins ordered in an unstable direction is an example of a false vacuum that decays via excitation of internal spin waves. Coupled evolution of the particle's magnetization (or the vacuum state) and spin waves, considered in the time-dependent vacuum frame, leads to a peculiar relaxation that is very fast at the beginning but slows down to a nonexponential long tail at the end. The two main scenarios are linear and exponential spin-wave instabilities. For the former, the longitudinal and transverse relaxation rates have been obtained analytically. Numerical simulations show that the particle's magnetization strongly decreases in the middle of reversal and then recovers.
Heat capacity data on Mn12 are fitted within the extended Debye model that takes into account a continuum of optical modes as well as three different speeds of sound.
The phonon-bottleneck problem in the relaxation of two-level systems (spins) via direct phonon processes is considered numerically in the weak-excitation limit where the Schroedinger equation for the spin-phonon system simplifies. The solution for the relaxing spin excitation p(t), emitted phonons n_k(t), etc. is obtained in terms of the exact many-body eigenstates. In the absence of phonon damping Gamma_{ph} and inhomogeneous broadening, p(t) approaches the bottleneck plateau p_\infty > 0 with strongly damped oscillations, the frequency being related to the spin-phonon splitting Delta at the avoided crossing. For any Gamma_{ph} > 0 one has p(t) -> 0 but in the case of strong bottleneck the spin relaxation rate is much smaller than Gamma_{ph} and p(t) is nonexponential. Inhomogeneous broadening exceeding Delta partially alleviates the bottleneck and removes oscillations of p(t). The line width of emitted phonons, as well as Delta, increase with the strength of the bottleneck, i.e., with the concentration of spins.
Magnetic nanoparticles with Neel surface anisotropy, different internal structures, surface arrangements and elongation are modelled as many-spin systems. The results suggest that the energy of many-spin nanoparticles cut from cubic lattices can be represented by an effective one-spin potential containing uniaxial and cubic anisotropies. It is shown that the values and signs of the corresponding constants depend strongly on the particle's surface arrangement, internal structure and elongation. Particles cut from a simple cubic lattice have the opposite sign of the effective cubic term, as compared to particles cut from the face-centered cubic lattice. Furthermore, other remarkable phenomena are observed in nanoparticles with relatively strong surface effects: (i) In elongated particles surface effects can change the sign of the uniaxial anisotropy. (ii) In symmetric particles (spherical and truncated octahedral) with cubic core anisotropy surface effects can change its sign. We also show that the competition between the core and surface anisotropies leads to a new energy that contributes to both the 2nd- and 4th-order effective anisotropies.
We study magneto-elastic effects in crystals of magnetic molecules. Coupled equations of motion for spins and sound are derived and the possibility of strong resonant magneto-acoustic coupling is demonstrated. Dispersion laws for interacting linear sound and spin excitations are obtained for bulk and surface acoustic waves. We show that ultrasound can generate inverse population of spin levels. Alternatively, the decay of the inverse population of spin levels can generate ultrasound. Possibility of solitary waves of the magnetization accompanied by the elastic twists is demonstrated.
Theory of magnetic deflagration (avalanches) in crystals of molecular magnets has been developed. The phenomenon resembles the burning of a chemical substance, with the Zeeman energy playing the role of the chemical energy. Non-destructive reversible character of magnetic deflagration, as well as the possibility to continuously tune the flammability of the crystal by changing the magnetic field, makes molecular magnets an attractive toy system for a detailed study of the burning process. Besides simplicity, new features, as compared to the chemical burning, include possibility of quantum decay of metastable spin states and strong temperature dependence of the heat capacity and thermal conductivity. We obtain analytical and numerical solutions for criteria of the ignition of magnetic deflagration, and compute the ignition rate and the speed of the developed deflagration front.
The problem of the phonon bottleneck in the relaxation of two-level systems (spins) to a narrow group of resonant phonons via emission-absorption processes is investigated from the first principles. It is shown that the kinetic approach based on the Pauli master equation is invalid because of the narrow distribution of the phonons exchanging their energy with the spins. This results in a long-memory effect that can be best taken into account by introducing an additional dynamical variable corresponding to the nondiagonal matrix elements responsible for spin-phonon correlation. The resulting system of dynamical equations describes the phonon-bottleneck plateau in the spin excitation, as well as a gap in the spin-phonon spectrum for any finite concentration of spins. On the other hand, it does not accurately render the lineshape of emitted phonons and still needs improving.